When four coins are tossed simultaneously, In number of the outcomes at two of the cpins will turn up as head? 1 17, 2 28, 3 11, 4 43

The volume of the solid generated will be 201 cubic units

Let's rotate it around the y-axis rather than x = 0.

(x-5)² = 4 - y → y = 4 - (x - 3)²

The parabolic section's area is A.

= 2 · int_0^2 (4 - x²) dx = 2(4x - x^3/3)|_0^2 = 32/3

At x, there is a horizontal centroid.

x = 3, so C = 2π(3) = 6π

V = A · C = 32/3 · 6π = 64π cubic units.

Cylinder method: V = 2π int_1^5 (4x - x(x-3)²)) dx = 2π int_1^5(-x^3 +6x² - 5x) dx

V = 2π(-x^4/4 + 2x^3 - 5x²/2)|_1^5 = 2π[(-625/4 + 250 -125/2) - (-¼ + 2 - 5/2)]

V = 2π(125/4 + 3/4) = 2π(32) = 64π cubic units

About 201 cubic units.

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The question would be:

What is the volume of the solid generated when the region bounded by the curve (x-5) ^2 =4-y and the x-axis is revolved around the line x=2?

Answer:

5491.50575

Step-by-step explanation:

10520 x (1 - 0.15)^4
so first you subtract 1 from 0.15 and that equals 0.85 then you times 0.85 itself cuz it decreases value for a total of four years and that would make 0.85^4 =0.52200625 now you 10520 x 0.52200625= 5491.50575
ps. depending if your adding or subtracting percents it will either 1+ or 1- then whatever percent into decimal hope this helps!

Frequency table is provided in image and mean=57.28, mode=63 and meadian=61.5.

What is a frequency table ?

A frequency table consists of the lists of items in a given data set and the number of times each item occurs in the data set and The number of times a particular data value occurs in a given data set is referred to as its frequency.

e.g.

A, A, A, B, B, B, B, C, C, D

Count the number of times each grade occurs in the above series. Yes, ‘A’ occurs thrice, ‘B+’ occurs four times, ‘C’ occurs twice, and ‘D’ occurs once. Now, according to the definition of frequency, we can note the frequency of each grade as follows:

Frequency of A = 3

Frequency of B = 4

Frequency of C = 2

Frequency of D = 1

Let us list the grades obtained by the students in the above example, in a frequency table. Table is in image.

Now,

For given frequency table

Mean=sum of all values/no. of terms=2864/50=57.28

Mode=63 as the frequency is highest for 63

Median=(25th+26th) terms/2=61.5.

Hence,

           mean=57.28, mode=63 and meadian=61.5.

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Answer:

 (28800 cm2) / (400 cm2/tile) = 72 tiles

Step-by-step explanation:

About 68% of the area is covered by one standard deviation above and below the mean, therefore one standard deviation above the mean corresponds to 34% of the area. Thus, we have 84% after adding the 50% below the mean and the 34% above the mean.

A normality assumption with a zero mean and a standard error of one is referred to as the typical normally distributed. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.

Sixty-eight percent of the observations for the normal distribution are within one standard deviation of the mean, ninety-five percent are within two standard deviations of the mean, and ninety-nine percent are within three standard deviations of the mean.

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Answer:

y = 4 and lh = 16

Step-by-step explanation:

hi again

According to the exterior angle theorem, the exterior angle that results from stretching a triangle's side is equal to the sum of the dimensions of the triangle's two opposed interior angles.

According to the exterior angle theorem, the exterior angle that results from stretching a triangle side is equal to the sum of the dimensions of the triangle's two opposed interior angles. Three internal angles in a triangle or polygon always add up to 180 degrees. This theorem is applied to each of the outer angles, which total six.

Here,

Given :

With the help of the triangle's well-known features, we can validate the exterior angle theorem.

Think about an ABC.

The total of the three angles is 180 degrees (angle sum property of a triangle) ——- Equation 1: (A+B)/180 ——- Example 2 (rewriting equation 1)

e = 180 - c

——- Equivalent 3 (linear pair of angles)

Equation 3 may be solved for by substituting the value of c.

e = 180 - [180 - (a + b)]

e = 180 - 180 + (a + b)

e = a + b.

=> m∠A = m∠G

=> m∠DMG > m∠A

So , its proven that:

=> m∠DMG > m∠G

and

=> A-D-M

So,

AD = DM

=> AD <AM

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When taking out a loan, the borrower must provide collateral such as a car or home to reduce the risk to the lender and increase the chances of the loan being approved. This includes rent, monthly bus pass, savings, student loan payment, and other expenses.

A loan is a type of debt that is typically provided by a financial institution such as a bank, credit union, or finance company. The purpose of a loan is to provide the borrower with a large sum of money that they may not have readily available, which they must then pay back over a set period of time with interest.

There are various types of loans, including personal loans, car loans, home loans, and student loans. Personal loans are unsecured loans that can be used for a variety of purposes, such as debt consolidation or home improvement. Car loans are used specifically to purchase a vehicle, while home loans are used to purchase a home. Student loans are designed to help pay for education expenses.

When taking out a loan, the borrower is typically required to provide some form of collateral, such as a car or a home, to secure the loan. This helps to reduce the risk to the lender and increases the chances of the loan being approved.

1. Rent: 30% of $3,850 = $1,155.

2. Monthly bus pass for work: 11% of $3,850 = $423.

3. Savings: 10% of $3,850 = $385.

4. Student loan payment: 5% of $3,850 = $192.5.

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Hemostasis is the process that causes a blood vessel to stop bleeding. It is a multi-step process with connected steps.

Here are the right answers in the right sequence.

Hemostatic mechanisms come in THREE varieties.

First, a VASULAR spasm tightens the blood vessel that has ruptured, limiting bleeding.

A significant amount of platelets AGGREGATE and go through degranulation during the creation of platelet plugs.

DEGRANULATION AIDS IN HEMASTASIS

Blood turns from a liquid to a gel during COAGULATION, also known as clotting, creating a blood clot. Hemostasis, the stoppage of blood loss from a damaged vessel, and repair may be the outcomes. The activation, adhesion, and aggregation of platelets, as well as the deposition and maturation of fibrin, are all components of the coagulation process.

After an injury, coagulation starts virtually right after.

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Answer:

38°

Step-by-step explanation:

142° and x° are angles on a straight line. Angles on a straight line are equal to 180°

142° + x° = 180°

x° = 180° - 142°

x° = 38°

The monthly interest rate for the principal is 0.64%

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

The formula for compound interest is

A = P(1 + r/n)^(nt)

where:

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal form)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for

Since the annual interest rate (r) is 7.7%. The monthly interest rate can be calculated by dividing the annual interest rate by 12 (There are 12 months in a year).

Thus, monthly interest rate = 7.7 / 12 = 0.64%

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Answer:

176 miles

Step-by-step explanation:

Step 1: determine what 44% of 400 miles is

44% of 400= 176

Answer: Santiago fell asleep at 176 miles and they had 224 miles left in their trip.

Answer:

x = 7

Step-by-step explanation:

In a triangle(3 sides), the total number of degrees is 180 degrees.

In a quadrilateral(4 sides), the total number of degrees is 360 degrees.

^^ Now convert this into a formula

Let's say s = number of sides

d = total degrees

s:       d:

3 --> 180

4 --> 360

Hence, the relation between s and d is:

(s-2)*180

Let's test this relation:

3:

(3-2)*180 =  ==> plugin 3 for s in (s-2)*180

1*180 = 180 √

4:

(4-2)*180 =  ==> plugin 4 for s in (s-2)*180

2*180 = 360 √

Now apply this formula to an 8-sided figure:

s = 8

(s-2)*180 =

(8-2)*180 =   ==> plugin 8 for s in (s-2)*180

6*180 = 1080 total degrees in the 8-sided figure

Since all 8 sides in the 8-sided figure are equal, all 8 angles are equal as well.

Hence, the measure of each angle is:

1080 / 8 = 135 degrees

Hence:

16x + 23 = 135  ==> solve for x

16x = 112  ==> subtract 23 on both sides to isolate x

x = 7  ==> divide both sides by 16 to isolate x

The answer is C. There is a positive linear relationship between player height and number of points scored for basketball players in the coach's state.

A confidence interval is a range of values that is calculated from the data and is believed to contain the true population parameter with a certain level of confidence, in this case 96%. The slope of the regression line is the average change in y for a one unit change in x, which represents the direction and strength of the relationship between x and y.

The confidence interval for the slope is (−0.432,1.844), which does not include 0, which means that the slope is not equal to 0. If the slope were 0, there would be no relationship between player height and points scored. The fact that the confidence interval is positive means that the slope is positive, which indicates a positive linear relationship between player height and number of points scored.

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The volume of the solid generated by revolving the region bounded by y = 2x - x^2 and y = x about the line x=1 can be found using the method of cylindrical shells. The method involves slicing the solid into thin cylindrical shells, finding the volume of each shell, and then summing the volumes of all the shells to find the total volume of the solid.

We start by finding the equations for the two curves:

y = 2x - x^2,

y = x

We then find the points of intersection between the two curves:

2x - x^2 = x

x^2 - x - 2 = 0

x = 2 or x = -1

Since the solid is generated about the line x=1, we only consider the part of the region that lies to the right of x=1, which corresponds to x=2. The radius of each cylindrical shell is equal to the difference between the x-coordinate of the upper curve and x=1, which is 1. The height of each shell is equal to the difference between the y-coordinates of the two curves at x=2, which is (2x - x^2) - x = 2 - 4 = -2.

The volume of cylindrical shell is:

V = πr^2h

Plugging in the values:

V = π * (1^2) * (-2)

V = -2π

The total volume of the solid is the sum of the volumes of all the cylindrical shells, which is just -2π. The volume is negative because the height of each shell is negative, which indicates that the solid is being generated in the opposite direction.

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Answer: It's D

Step-by-step explanation:

In a case whereby one solution contains 2 parts salt to 8 parts water, and another contains 3 parts salt 5 parts water.  the number of each part that should be mixed together in order to obtain 280 quarts of a solution that is 3 parts salt to 7 parts water are: x = 160 quarts and 120 quarts  respectively.

The concept that will be used here is simplification

The salt concentration  can be expressed by turning them to decimal form and these area;

Solution A: [2/(2 + 8)]

= [2/10]

= 0.20 salt

We can as well expresss the Solution B in term of fraction as:

: [3/(3 + 5) ]

= [3/8 ]

= 0.375 salt

We can as well express the Mixed Solution in term of fraction we can be done as

:[ s/(3 + 7)]

= 3/10

= 0.30 salt

The mixture is said to be 280 quarts, however in the case whereby  0.375 salt can found in the mixed solution that is denoted as " x" , we can know the  0.20 salt,  which can be expressed as [y = 280 – x]

Then we can compute the typical mixture equation as :

[0.375x + 0.20(280-x)]  = [0.30(280)]

If we simplify we have

[0.375x + 56 - 0.20x] = 84

It can be simplied further as

[0.375x - 0.20x + 56 – 56] = [84 – 56]

Then after the summation from the left sides we have

[0.375x - 0.20x] = 28

[0.175x ]= 28

Then, we can find the value of x as

x= 28/0.175

x = 160

Since the value of x is known we can find the value of Y as :

y = [280 – x]

y = [280 – 160]

Then the value of  y can be expressed as :

y = 120

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The simple events in this ranking experiment are C-D-P, C-P-D, D-C-P, D-P-C, P-C-D, P-D-C where all of the simple events have the same probability, 1/6.

The simple events in this ranking experiment are the 6 possible ways the individual can order the three glasses of cola: C-D-P, C-P-D, D-C-P, D-P-C, P-C-D, P-D-C.

Since the individual's preferences are assumed to be random and the same cola has been put into all three glasses labeled C, D, and P, each of the 6 possible ways the individual can order the glasses (C-D-P, C-P-D, D-C-P, D-P-C, P-C-D, P-D-C) are equally likely.

This means that each of the 6 simple events has a probability of 1/6, or 0.1667. This is because if each ordering of the glasses is considered an outcome, there are 6 equally likely outcomes. The probability of any one of the outcomes is 1 divided by the total number of outcomes, or 1/6.

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Cost of the item in both cases are (a) $21 (b) $21.6 and (c) Lower price of the item is when applied 20% discount first and then $3 off.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

(a) Original price of the item = $30

After 20% discount, price of the item = 30 - (30 × 20%)

                                                              = 30 - (30 × 0.2)

                                                              = $24

After $3 off, price of the item = $24 - $3 = $21

(b) Original price of the item = $30

After $3 off, price of the item = $30 - $3 = $27

After 20% discount, price of the item = 27 - (27 × 20%)

                                                             = $21.6

(c) The lower price is when applied 20% discount first and then $3 off.

Hence the price of the item is lower when we apply 20% discount first and then applied $3 off.

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With 99% confidence that the true difference lies between 0.1316 and 0.2694.

A 99% confidence interval for the difference in average SAT scores between coached and uncoached students can be constructed using the data above.

The confidence interval is calculated as (mean of coached students - mean of uncoached students) +/- (2 * standard error of the difference in means).

The mean of coached students is (0.3098 + 0.3399 + 0.219 + 0.0798) / 4 = 0.2155, and the mean of uncoached students is (0.0046 + 0.0248) / 2 = 0.0147. The standard error of the difference in means can be calculated as the square root of ((0.2155(1-0.2155)/4) + (0.0147(1-0.0147)/2)).

The confidence interval is then (0.2155 - 0.0147) +/- (2 * 0.0347) = 0.201 +/- 0.0694, or (0.1316, 0.2694). This indicates that, on average, coached students gain 0.201 points more than uncoached students, with 99% confidence that the true difference lies between 0.1316 and 0.2694.

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By graph, the solution of the system of equations is (- 1, - 3).

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The system of equations are,

⇒ y - 2x - 1

⇒ y = - 3x - 6

Now, We can draw the graph of given system of equations.

The red line shows the graph of y = 2x - 1 and blue line shows the graph of y = - 3x - 6.

So, By graph;

Both equations are cut into at point (- 1 , - 3).

Hence, By graph, the solution of the system of equations is (- 1, - 3).

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The equations for price of one tire patch

4x + 1.9 = 22.2

22.2 – 4x = 1.9

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We have to find the Equation for  price of one tire patch.

Ryan bought 4 tire patches.

Price on gift card= $22.2

Then, according situation the equations for price of one tire patch

4x + 1.9 = 22.2

and, 22.2 – 4x = 1.9

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The range of possible side lengths that satisfy these conditions is,

⇒ { s | 45.5 < s < 49.5 }

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The perimeter of a square must be greater than 182 inches but less than 198 inches.

Now, We know that;

The perimeter of a square is given by,

⇒ P = 4s

Where, 's' represents the length of a side.

Here, The perimeter of a square must be greater than 182 inches but less than 198 inches.

Hence, We get;

⇒ 182 < P < 198

Since, P = 4s

⇒ 182 < 4s < 198

⇒ 182/4 < 4s/4 < 198/4

⇒ 45.5 < s < 49.5

Thus, The range of possible side lengths that satisfy these conditions is,

⇒ { s | 45.5 < s < 49.5 }

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Answer:

[A] 1406

Step-by-step explanation:

To see which is NOT divisible by 8 all we have to do is divide each answer choice by 8.

Not divisible means that the answer is a whole number (Not a decimal).

[A] 1406/8 = 175.75

[B] 1488/8 = 186

[C] 3608/8 = 451

[D] 5016/8 = 627

As we can see, the only one that is not divisible by 8 is [A] 1406.

RevyBreeze

Answer:

V = 31,667.8 cubic ft

Step-by-step explanation:

The volume of a right circular cone can be calculated using the formula:

V = (π * r^2 * h) / 3

Where r is the radius of the base and h is the height of the cone.

First, let's find the radius:

r = diameter / 2 = 18.7 ft / 2 = 9.35 ft

Now, we can plug in the values for r and h into the formula:

V = (π * 9.35^2 * 19) / 3 = (π * 87.5295 * 19) / 3 = (1670.20355 * 19) / 3 = 31,667.76 cubic ft

Rounding to the nearest tenth of a cubic foot, we get:

V = 31,667.8 cubic ft

Based on the histogram, 13 students held their breath for greater than 12.5 seconds but less than 15.5 seconds.

In a first-grade class, students measured how long they could hold their breath. The results were shown on a graph called a histogram. To see how many students held their breath between 12.5 and 15.5 seconds, we need to look at the bars on the graph between those times. The number of students is shown by the height of each bar.

We can see that there are 2 students who held their breath between 12.5 and 13.5 seconds. There are 5 students who held their breath between 13.5 and 14.5 seconds. And there are 6 students who held their breath between 14.5 and 15.5 seconds. To find out the total number of students, we add the heights of the bars together.

So:

Hence, there are 13 students who held their breath between 12.5 and 15.5 seconds.

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The smallest number of units that must be sold for the company to realize a profit will be 3,637 units.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

To produce each product unit, the company spends $1.75 on material and $2.95 on labor. Its total fixed cost is $6000. Each unit sells for $6.35.

Let 'x' be the number of units. Then the equation is given as,

6.35x = 1.75x + 2.95x + 6000

Simplify the equation, then we have

6.35x = 1.75x + 2.95x + 6000

6.35x = 4.7x + 6000

1.65x = 6000

x = 3637 units

The smallest number of units that must be sold for the company to realize a profit will be 3,637 units.

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